Economania is a closed island economy where two goods A and B are each produced by many identical perfectly competitive firms using labor L and some input X according to standard production functions. If all these goods were pure private goods, what is the necessary condition for Pareto optimality with respect to assigning X and L to produce the two goods? Why would the competitive equilibrium satisfy this condition? Assume instead that the use of input X to produce A causes harm to industry B. That is, an increase in X used to prod

The market for corn in country a is highly competitive. at the current market price of $5/bushel there is a shortage of 100,000 bushels of corn in this country. media reports claim that the price of corn will rise drastically in the near future. according to these reports, the neighboring country b had witnessed a similar situation recently. at the same price, the shortage in country b was also 100,000 bushels and eventually the equilibrium price in b went up to $10/bushel. both countries are known to have equal number of corn producers and the market supply of corn is identical at all prices. this, combined with the fact that consumers in the two countries also have similar tastes and preferences, led the media to conclude that the price of corn in country a would soon be as high as $10/bushel. the new equilibrium price turns out to be below $10/bushel, what inferences can be drawn?

Bakery has bought 250 pounds of muffin dough. they want to make waffles or muffins in half-dozen packs out of it. half a dozen of muffins requires 1 lb of dough and a pack of waffles uses 3/4 lb of dough. it take bakers 6 minutes to make a half-dozen of waffles and 3 minutes to make a half-dozen of muffins. their profit will be $1.50 on each pack of waffles and $2.00 on each pack of muffins. how many of each should they make to maximize profit, if they have just 20 hours to do everything?

True or false: a fitted model with more predictors will necessarily have a lower training set error than a model with fewer predictors.